Step 1:

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The function is $\"\"$ and point is $\"\"$ .

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From gradient vector, $\"\"$ .

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Consider $\"\"$ .

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Apply partial derivative on each side with respect to $\"\"$ .

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$\"\"$

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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Apply partial derivative on each side with respect to $\"\"$ .

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$\"\"$

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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Then the gradient vector is $\"\"$ .

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Step 2:

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The maximum rate of change of a function $\"\"$ at a point $\"\"$ occurs in the direction is $\"\"$ .

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The magnitude of $\"\"$ is the maximum rate of change.

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The maximum rate of change of a function $\"\"$ at a point $\"\"$ occurs in the direction is

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$\"\"$ .

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The magnitude of $\"\"$ is $\"\"$ .

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Solution :

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The maximum rate of change is 1.

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The direction of the maximum rate of change is $\"\"$ .